Thesis DefenseTuesday July 16th, 2019 Time: 12:30 PM Title: Rotationally Symmetric Extremal Kähler Metrics Speaker: Selin Taşkent, Stony Brook University Location: Math Tower 5-127 Abstract: In this thesis, we provide a complete list of rotationally symmetric extremal Kähler metrics on $C^n$ ($n>=2$)and $C^2$\{0}.We give necessary and sufficient conditions for adding a smooth point at the origin in $C^n$. As an application, we show the existence of new families of extremal Kähler metrics with orbifold and cone angle singularities, We also show certain solutions on $C^2$\{0} can be completed to give metrics on complex line bundles over $CP^1$.